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Jordan Stoyanov, Probability measures and their moment (in)determinacy: Results and open questions

Datum objave: 25. 3. 2016
Seminar za algebro in funkcionalno analizo
Četrtek, 31. 3. 2016, ob 12:30 v predavalnici 2.04, FMF, Jadranska 21, Ljubljana
The discussion will be on and around the following fundamental fact: Any probability measure with all moments finite is either uniquely characterized by its moment sequence (M-determinate) or it is non-unique (M-indeterminate). Well-known are classical results by Stieltjes, Carleman, Cramer, Hausdorff, Krein, Berg, … In this talk the emphasis will be on some very recent developments (Hardy’s condition, rate of growth of the moments, Stieltjes classes). Further progress can be made if we are able to answer a list of open questions about the moment determinacy of probability measures in both dimension 1 and n. These are questions from real or complex Analysis (e.g. dealing with systems of functional integral equations, Fourier transform, factorization of measures, denseness of polynomials in some spaces) and Algebra (e.g. dealing with infinite systems of algebraic equations). A few statements will be reported to show that new ideas and techniques are needed to challenge the open questions. Any suggestion made during the talk or later will be more than welcome.